US8693386B2 - Resource allocation for orthogonal decode-and forward-input multiple-output relay channels with finite rate feedback - Google Patents

Resource allocation for orthogonal decode-and forward-input multiple-output relay channels with finite rate feedback Download PDF

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US8693386B2
US8693386B2 US13/138,043 US200913138043A US8693386B2 US 8693386 B2 US8693386 B2 US 8693386B2 US 200913138043 A US200913138043 A US 200913138043A US 8693386 B2 US8693386 B2 US 8693386B2
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node
source
relay
state information
channel state
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Jun Xiao
Wen Gao
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Thomson Licensing SAS
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/38—Transceivers, i.e. devices in which transmitter and receiver form a structural unit and in which at least one part is used for functions of transmitting and receiving
    • H04B1/3822—Transceivers, i.e. devices in which transmitter and receiver form a structural unit and in which at least one part is used for functions of transmitting and receiving specially adapted for use in vehicles

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  • the present invention generally relates to communications systems and, more particularly, to wireless systems, e.g., terrestrial broadcast, cellular, Wireless-Fidelity (Wi-Fi), satellite, etc.
  • wireless systems e.g., terrestrial broadcast, cellular, Wireless-Fidelity (Wi-Fi), satellite, etc.
  • CSI channel state information
  • a near-optimal resource allocation method is provided for a Multiple-Input Multiple-Output (MIMO) relay scheme in which the source and relay nodes have only partial channel state information (CSI), obtained through finite rate feedback, and the power of the source and relay nodes is constrained.
  • Power on/off beamforming is employed at the source and relay nodes in which the receiving node feeds back the identity of a beamforming matrix selected in accordance with the channel state.
  • the exemplary method allocates time between the first and second stages of the relay transmission, and power between the source and the relay nodes.
  • resource allocation is carried out by a scheduler at the source node operating in accordance with the method.
  • FIGS. 1A and 1B show schematic representations of the first and second stages, respectively, of a half-duplex orthogonal decode-and-forward MIMO relay arrangement
  • FIG. 2 is a flowchart of an exemplary method of allocating resources for a half-duplex orthogonal decode-and-forward MIMO relay arrangement in which the source and relay nodes are subject to a total power constraint;
  • FIG. 3 is a flowchart of a further exemplary method of allocating resources for a half-duplex orthogonal decode-and-forward MIMO relay arrangement in which the source and relay nodes are subject to individual power constraints.
  • FIGS. 1A and 1B show a schematic representation of an exemplary Multiple-Input Multiple-Output (MIMO) relay wireless communication arrangement 100 comprising source node S, relay node R and destination node D.
  • destination node D may be a mobile station, with source node S and relay node R being stationary, although any combination of stationary and mobile nodes is contemplated.
  • half-duplex, orthogonal, decode-and-forward MIMO relay channels are used with finite-rate channel state information (CSI) feedback. Being half-duplex, the relay node does not receive and transmit signals simultaneously. As such, each downstream transmission frame is split into two stages: a first stage, depicted in FIG.
  • relay node R receives and a second stage, depicted in FIG. 1B , in which relay node R transmits.
  • source node S transmits in the first stage but does not transmit in the second stage.
  • Destination node D receives throughout the downstream frame, from source node S in the first stage and from relay node R in the second stage.
  • Source node S has multiple transmit antennas
  • relay node R has multiple antennas which are used to receive and transmit
  • destination node D has multiple receive antennas. Each antenna may be used to transmit or receive or to transmit and receive.
  • source node S also includes a scheduler for allocating resources in the relay communications arrangement 100 .
  • the scheduler allocates time between the first stage and the second stage, and power between the source and the relay nodes based on channel statistical information (e.g., path loss factors or coefficients, distributions of the channel matrices between the source and relay nodes, between the relay and destination nodes, and between the source and destination nodes) and finite rate CSI feedback.
  • channel statistical information e.g., path loss factors or coefficients, distributions of the channel matrices between the source and relay nodes, between the relay and destination nodes, and between the source and destination nodes
  • finite rate CSI feedback finite rate CSI feedback
  • Y r ⁇ square root over ( ⁇ sr ) ⁇ H sr X s +W 1 (1)
  • Y d,1 ⁇ square root over ( ⁇ sd ) ⁇ H sd X s +W 2 (2)
  • Y r and Y d,1 are the received signals at relay node R and at destination node D respectively;
  • ⁇ sr and ⁇ sd are the path loss coefficients for the source-relay and source-destination links, respectively;
  • H sr and H sd are the channel matrices for the source-relay and source-destination links, respectively;
  • X s is the signal transmitted from source node S; and
  • W 1 and W 2 are additive white Gaussian noise vectors with zero mean and identity matrix (I) covariance.
  • the dotted arrow represents a limited bandwidth channel from relay node R to source
  • FIG. 1B shows that in the second stage, only relay node R transmits.
  • X r is the signal transmitted from relay node R
  • ⁇ rd is the path loss coefficient between the relay and destination nodes
  • H rd is the channel matrix between the relay and destination nodes
  • W 3 is an additive white Gaussian noise vector with zero mean and identity matrix covariance.
  • the dotted arrow represents a limited bandwidth CSI feedback channel from destination node D to relay node R.
  • a Rayleigh block independent identically distributed (i.i.d.) fading channel model is assumed; i.e., the channel matrices H are independent from block to block but constant within a block.
  • the duration of a block is on the order of microseconds.
  • a power on/off beamforming strategy is employed for the CSI feedback.
  • the transmitting node will apply power to selected ones of its multiple transmit antennas to generate “on” beams in accordance with a beamforming matrix selected from a codebook.
  • the codebook may be designed, for example, using quantization on Grassmann manifolds in accordance with known techniques.
  • the beamforming matrix is selected in accordance with CSI fed-back from the receiving node.
  • the CSI fed-back from the receiving node may include an explicit identification of which beamforming matrix to use (e.g., a matrix index or identifier) or information indicative of the channel state from which the transmitting node can determine the optimal beamforming matrix to use for the given channel conditions.
  • the beamforming matrix is determined in accordance with the CSI feedback from the receiving node. As described above, CSI is fed back from relay node R to source node S in the first stage ( FIG. 1A ) and from destination node D to relay node R in the second stage ( FIG. 1B ).
  • the proportion of time of a transmission frame for the duration of the first stage is denoted herein as ⁇ , and for the second stage 1 ⁇ , with 0 ⁇ 1.
  • ⁇ is the total transmission power of source node S and relay node R
  • P s and P r are the transmission powers at source node S and relay node R, respectively.
  • the achievable transmission rate e.g., bits/sec
  • FIG. 2 is a flowchart of an exemplary method of allocating resources for a half-duplex orthogonal decode-and-forward MIMO relay arrangement in which the source and relay nodes are subject to a total power constraint.
  • the method is based on a near-optimal solution for the parameters s, ⁇ and ⁇ of Eq. 6. This method may be carried out by a scheduler, for example, located at source node S, as shown in FIGS. 1A and 1B .
  • the resource allocation method is initiated, for example, when channel conditions change, such as a result of a change in position of destination node D. Such an event will usually be reflected in a change in the path loss coefficients of the channels and can be detected at the receiving node (e.g., the destination node).
  • the relay and/or destination nodes can periodically estimate the path loss coefficients and feed them back to the scheduler. The scheduler can then determine whether a new resource allocation is required and if so, perform the exemplary resource allocation method.
  • step 202 various parameters to be used in carrying out the resource allocation method are obtained (e.g., read from storage, received, measured), including, for example, the network configuration, constraints on the source and relay power for the links in question (e.g., total power), channel statistical information (e.g. path loss factors, channel matrix probability distributions) for the three links between nodes S, R and D, and the feedback channel rates from node R to node S and node D to node R.
  • various parameters to be used in carrying out the resource allocation method are obtained (e.g., read from storage, received, measured), including, for example, the network configuration, constraints on the source and relay power for the links in question (e.g., total power), channel statistical information (e.g. path loss factors, channel matrix probability distributions) for the three links between nodes S, R and D, and the feedback channel rates from node R to node S and node D to node R.
  • the network configuration e.g., constraints on the source and relay power for the links in question (e.g
  • the scheduler need only know the statistics or the probability distribution of each channel matrix H, as opposed to H itself (or an estimate of H), in order to determine the resource allocation (values for s, ⁇ , and ⁇ ).
  • the statistics for the channel between a transmitting node and a receiving node can be obtained using a special training phase in which the transmitting node sends to the receiving node a known training signal from which the receiving node can estimate the channel using known techniques.
  • the receiving node feeds back the estimate of the channel to the scheduler which extracts the statistics of the channel for carrying out resource allocation.
  • step 210 out of a plurality of possible combinations of the number of “on” beams s one such combination is chosen. Note that since s 3 equals the minimum of s 1 and the number of receiving antennas at destination node D, the possible combinations of the values of s is actually determined by s 1 and s 2 , the numbers of on-beams used in the first and second stages, respectively.
  • step 210 because combination optimization is extremely hard and I 1 and I 2 are not necessarily differentiable functions about s, an exhaustive search of all possible combinations of values for s is carried out in the exemplary method. Note, however, that the burden of such a search should be manageable because each value of s is at most equal to the number of receive antennas, typically a small number.
  • the allocation of resources will typically only need to be updated when the position of a mobile destination node changes.
  • the number s for a transmitting node is a monotonically increasing function of power. Therefore, in some scenarios it is not necessary to exhaustively search over a number of different values. For example, in the case of a link with low signal-to-noise ratio (SNR), the value of the corresponding parameter s (i.e., s 1 for the S-R link, s 2 for the R-D link, and s 3 for the S-D link) is 1, and in the case of a link with high SNR, the corresponding s is equal to the number of receive antennas.
  • SNR signal-to-noise ratio
  • a reason that lower number of “on” beams is used when the SNR is low is that each “on” beam would be stronger with a given power allocated to a node.
  • the SNRs can be obtained in a training session and the training should be performed from time to time just in case that the SNRs change significantly.
  • step 211 initial values for ⁇ and/or ⁇ are determined based on approximations of SNR for the three links between the source, relay and destination nodes (i.e., S-R, R-D and S-D).
  • SNR of each link is approximated as being “high” or “low,” with initial values for ⁇ and/or ⁇ being determined based on the combination of SNR approximations.
  • all (seven) meaningful combinations of SNR approximations (see Table 1) for the three links are considered in the exemplary method of FIG. 2 , with some combinations providing an initial value for ⁇ and some combinations providing an initial value for ⁇ .
  • step 212 the optimal value for ⁇ that maximizes the achievable rate R is determined for a given value of ⁇ and the optimal value for ⁇ that maximizes the achievable rate R is determined for a given value of ⁇ .
  • I 1 is a monotonically increasing function about ⁇
  • I 2 is a concave function about ⁇ .
  • the maximum rate is achieved at either the maximum point of I 2 or the cross point of I 1 and I 2 .
  • the maximum point, ⁇ m arg max(I 2 ), can be obtained from the root of
  • s 2 ⁇ k 3 ⁇ ⁇ s 3 ⁇ ⁇ 1 - cos ⁇ ( 2 ⁇ t ) 1 + r 2 2 - 2 ⁇ r 2 ⁇ cos ⁇ ( t ) ⁇ d t , ( 7 ⁇ b )
  • m ij min(L T i ,L R i )
  • n ij max(L T i ,L R i )
  • L T i and L R i are the number of transmitting and receiving antennas, respectively, of node i
  • r 2 ⁇ square root over (max(s 3 ,L R d )/s 3 ) ⁇
  • r 3 ⁇ square root over (n rd /m rd ) ⁇ .
  • the optimal value for ⁇ that maximizes the achievable rate R is determined using the optimal value for ⁇ just obtained.
  • the properties of I 1 and I 2 described above for the determination of the optimal value of ⁇ apply for the determination of the optimal value of ⁇ .
  • the maximum rate is achieved at either the maximum point of I 2 or the cross point of I 1 and I 2 .
  • step 214 a determination is made as to whether there is convergence to a local optimal point given the values determined in step 212 . If not, step 212 is repeated until convergence is achieved. Convergence can be considered to have occurred, for example, if the improvement in achievable rate R after an iteration of step 212 is less than a given threshold value.
  • step 215 a determination is made as to whether all of the combinations of SNR approximations (see Table 1) for the three links S-R, R-D and S-D have been exhausted. If not, operation loops back to step 211 in which a new combination of SNR approximations is selected to obtain a new initial value for ⁇ or ⁇ . Steps 212 and 214 are repeated as described above using the new initial value for ⁇ or ⁇ . Once it is determined at step 215 that all combinations of SNR approximations have been exhausted, operation proceeds to step 216 , at which a determination is made as to whether all the combinations of values for s have been exhausted.
  • step 216 operation loops back to step 210 to choose another combination of values for s and steps 211 , 212 , 214 and 215 are repeated, as described above. If it is determined at step 216 that all combinations of values for s have been exhausted, operation proceeds to step 217 in which the optimal set of values for s, ⁇ and ⁇ , i.e., the set of values generated by the above-described iterative process that provides the highest achievable rate R, are provided by the scheduler to the nodes for implementation. More specifically, in the exemplary relay arrangement described above, the parameters s, ⁇ , and ⁇ are provided to the transmitting nodes (source S and relay R). s 1 is provided to the relay node and s 2 is provided to the destination node.
  • ⁇ is provided to both the relay and the destination nodes in order to synchronize their transmission and reception. It should be noted that if SNR approximation from a training session is used in step 211 , step 215 can be eliminated. Furthermore, the process as shown in FIG. 2 can be repeated in response to a change in SNRs obtained from a new training session.
  • the receiving nodes select the beamforming matrix to be used by the respective transmitting node (source S or relay R) in the following transmission and then feedback the identity of the matrix to the transmitting node.
  • the beamforming matrix to be used by S is obtained at R and is fed-back to S for transmission.
  • the beamforming matrix to be used by R is obtained at D and is fed-back to R for transmission.
  • the resource allocation problem for the exemplary half-duplex orthogonal decode-and-forward MIMO relay arrangement described above is generally non-convex and the exemplary method will converge to a local optimal point after a few iterations (e.g., five).
  • a few iterations e.g., five
  • many randomly selected initial points may be used or, preferably, just a few or even one good initial point.
  • the SNR of each of the S-D, R-D and S-R links can be approximated as being either “high” (e.g., ln(1+SNR) ⁇ ln(SNR)) or “low” (e.g., ln(1+SNR) ⁇ SNR) in order to separate the influence in Eq. 6 of the channel parameters from ⁇ and ⁇ .
  • ⁇ and ⁇ are unknown, however, it is not possible to know in advance whether a link is a high or a low SNR link (see Eq. 6). Therefore, as described above, all meaningful combinations of high and low SNR approximations for the three links are considered in order to find the combination which yields the best resource allocation.
  • initial values for ⁇ or ⁇ can then be determined for various combinations of high and low SNR approximations for the three links.
  • Initial values for ⁇ and/or ⁇ for seven different cases (1-7) of link SNR can be determined as set forth below in TABLE 1.
  • steps 211 - 215 are repeated for each of the seven cases listed in TABLE 1.
  • each node has an individual average power constraint P i , regardless of the time duration allocated to each stage.
  • FIG. 3 is a flowchart of an exemplary resource allocation method for applications in which the value of ⁇ is fixed in accordance with the aforementioned power constraint.
  • Steps 301 , 302 and 310 are similar to steps 201 , 202 and 210 described above with respect to the method of FIG. 2 .
  • the optimal value for ⁇ is determined using a procedure similar to that described above with respect to step 212 for a given value of ⁇ .
  • step 316 a determination is made as to whether all the combinations of values for s have been exhausted. If not, operation loops back to step 310 to choose another combination of values for s. If all combinations of values for s have been exhausted, operation proceeds to step 317 in which the resultant values for s and ⁇ are provided to source node S and relay node R for implementation.
  • the source and the relay nodes are subject to a constant peak power constraint, regardless of the time duration allocated to each stage.
  • the achievable rate is given by:
  • s 3 m ⁇ r ⁇ ⁇ d ⁇ ⁇ k r ⁇ ⁇ d ⁇ ⁇ r ⁇ ⁇ d + ⁇ f r ⁇ ⁇ d ⁇ ( ⁇ ) ⁇ d ⁇ .
  • the optimal value of ⁇ can be obtained by following steps shown in FIG. 3 with step 316 skipped or eliminated. If ⁇ and s are held constant, the optimal value of ⁇ can be obtained by switching the roles of ⁇ and ⁇ in FIG. 3 with step 316 skipped or eliminated. If ⁇ and ⁇ are held constant, the optimal value of s can be obtained by following steps shown in FIG.
  • step 302 initializes the maximum bit rate to zero and step 313 is replaced by a step of computing the transmission rate with the given ⁇ and ⁇ and if the computed transmission rate is higher than the stored transmission rate replaces the stored transmission rate with the computed transmission rate. It should be noted that with these configurations, the optimal values thus obtained must be provided to nodes at step 317 .
  • the principles of the invention are applicable to various types of wireless communications systems, e.g., terrestrial broadcast, satellite, Wireless-Fidelity (Wi-Fi), cellular, etc. Indeed, the inventive concept is also applicable to stationary or mobile transmitters and receivers. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention.

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